Whether the statement, “if f is continuous at 5 and and , then ” is true or false.
The statement is true.
Theorem used: If f is continuous at b and , then .
Given that, f is continuous at 5 and and .
Here, f is a composition of two functions.
Take , and .
Obtain the limit of the function as x approaches 2.
Here, is a polynomial. So it is continuous everywhere. That is, .
Since f is continuous at 5 and then by theorem stated above (1)
Substitute in equation (1), .
Hence, the required proof is obtained.
Note that, is required to prove the result.
Thus, the given statement is true.
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